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Descartes, Rene (1596-1650)

Cogito Ergo Sum. "I think, therefore I am."

Discours de la Methode. 1637.

Descartes, Rene (1596-1650)

If we possessed a
thorough knowledge
of all the parts of
the seed of any
animal (e.g. man),
we could from that
alone, by reasons
entirely
mathematical and
certain, deduce the
whole conformation
and figure of each
of its members, and,
conversely, if we
knew several
peculiarities of
this conformation,
we would from those
deduce the nature of
its seed.

unknown

Descartes, Rene (1596-1650)

When writing about transcendental issues, be transcendentally clear.

In G. Simmons Calculus Gems. New York: McGraw Hill Inc., 1992.

Descartes, Rene (1596-1650)

These long chains of
perfectly simple and
easy reasonings by
means of which
geometers are
accustomed to carry
out their most
difficult
demonstrations had
led me to fancy that
everything that can
fall under human
knowledge forms a
similar sequence;
and that so long as
we avoid accepting
as true what is not
so, and always
preserve the right
order of deduction
of one thing from
another, there can
be nothing too
remote to be reached
in the end, or too
well hidden to be
discovered.

Discours de la
Methode. 1637.

Descartes, Rene (1596-1650)

I thought the following four [rules] would be enough, provided that I made a firm and constant resolution not to fail even once in the observance of them. The first was never to accept anything as true if I had not evident knowledge of its being so; that is, carefully to avoid precipitancy and prejudice, and to embrace in my judgment only what presented itself to my mind so clearly and distinctly that I had no occasion to doubt it. The second, to divide each problem I examined into as many parts as was feasible, and as was requisite for its better solution. The third, to direct my thoughts in an orderly way; beginning with the simplest objects, those most apt to be known, and ascending little by little, in steps as it were, to the knowledge of the most complex; and establishing an order in thought even when the objects had no natural priority one to another. And the last, to make throughout such complete enumerations and such general surveys that I might be sure of leaving nothing out.

Discours de la Methode. 1637.

Descartes, Rene (1596-1650)

I concluded that I might take as a general rule the principle that all things which we very clearly and obviously conceive are true: only observing, however, that there is some difficulty in rightly determining the objects which we distinctly conceive.

Discours de la Methode. 1637.

Descartes, Rene (1596-1650)

If I found any new truths in the sciences, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.

Discours de la Methode. 1637.

Descartes, Rene (1596-1650)

Each problem that I solved became a rule which served afterwards to solve other problems.

Discours de la Methode. 1637.

Descartes, Rene (1596-1650)

Of all things, good sense is the most fairly distributed: everyone thinks he is so well supplied with it that even those who are the hardest to satisfy in every other respect never desire more of it than they already have.

Discours de la Methode. 1637.

De Morgan, Augustus (1806-1871)

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.